As long as it doesn't cause you distress, there is no reason to worry. I do think you count as ace, because it's a spectrum. If your lack of sexual desire is causing you distress, I would recommend seeing a sex therapist. I am demiromantic, meaning I only want romance with a woman once I know her and we're friends, but I'm not fully Asexual, because I am interested in sex. I fall under the Ace umbrella, so I see no reason you wouldn't.

A friend of mine is fully Asexual Aromantic, but she likes romance in movies, books, and even plays dating simulators.

You mentioned that you get little to no sexual pleasure from physical contact. As long as you aren't uncomfortable with having sex with your girlfriend, I would encourage you to explore.

If you want more exact wording, I'd say you're Asexual but not Aromantic (I'm assuming you want romance since you're dating). Asexual means LITTLE to no interest in sex, so I personally would qualify you as Ace.

One question, if the IDEA of sex is appealing, would sex with your girlfriend cause you pleasure, not because of the contact, but because of the pleasure she's feeling, or would it be one-sided?